Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure

Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Aerosol and its radiative effects during the aeroradcity 2018 Moscow experiment

During the AeroRadCity-2018 spring aerosol experiment at the Moscow State University Meteorological Observatory the aerosol properties of the atmosphere and radiative aerosol effects were analyzed using a wide complex of measurements and model COSMO-ART simulations over Moscow domain. The program of measurements consisted of columnar aerosol AERONET retrievals, surface PM10, black carbon (BC) and aerosol gas precursors mass concentrations, as well as radiative measurements under various meteorological conditions. We obtained a positive statistically significant dependence of total and fine aerosol optical depth (AOD) mode (R2 ~0.4) with PM concentrations. This dependence has revealed a pronounced bifurcation point around PM10=0.04 mgm-3. The modelled BC concentration is in agreement with the observations and has a pronounced correlation with PM, but not with the AODs. The analysis of radiative effects of aerosol has revealed up to 30% loss for UV irradiance and 15% - for shortwave irradiance at high AOD in Moscow. Much intensive radiation attenuation is observed in the afternoon when remote pollution sources may affect solar fluxes at elevated boundary layer conditions. Negative (cooling) radiative forcing effect at the top of the atmosphere from -18 Wm-2 to -4 Wm-2 has been evaluated. Mean difference in visible AOD between urban and background conditions in Moscow and Zvenigorod was about 0.01 according to measurements and model simulations, while in some days the difference may increase up to 0.05. The generation of urban aerosol was shown to be more favorable in conditions with low intensity of pollutant dispersion, when mean deltaAOD550 was doubled from 0.01 to 0.02

Minimal surfaces and particles in 3-manifolds

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm\"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm\"uller space. These results are extended to ``quasi-Fuchsian'' manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles''. Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm\"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm\"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm\"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds. Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde

The treatment of migraines and tension-type headaches with intravenous and oral niacin (nicotinic acid): systematic review of the literature

BACKGROUND: Migraine and tension-type headaches impose a tremendous economic drain upon the healthcare system. Intravenous and oral niacin has been employed in the treatment of acute and chronic migraine and tension-type headaches, but its use has not become part of contemporary medicine, nor have there been randomized controlled trials further assessing this novel treatment. We aimed to systematically review the evidence of using intravenous and/or oral niacin as a treatment for migraine headaches, tension-type headaches, and for headaches of other etiologic types. METHODS: We searched English and non-English language articles in the following databases: MEDLINE (1966–February 2004), AMED (1995–February 2004) and Alt HealthWatch (1990–February 2004). RESULTS: Nine articles were found to meet the inclusion criteria and were included in this systematic review. Hypothetical reasons for niacin's effectiveness include its vasodilatory properties, and its ability to improve mitochondrial energy metabolism. Important side effects of niacin include flushing, nausea and fainting. CONCLUSION: Although niacin's mechanisms of action have not been substantiated from controlled clinical trials, this agent may have beneficial effects upon migraine and tension-type headaches. Adequately designed randomized trials are required to determine its clinical implications

Safety and Effectiveness of Pharmacologic Conversion of Atrial Fibrillation and Flutter: Results of Multicenter Trial. Part II: Assessment of Safety

Aim. We aimed to assess safety and effectiveness of class III antiarrhythmic drug Refralon for conversion of atrial fibrillation (AFib) and flutter (AFl) in post-registration trial and to compare data of primary center (National medical research center in cardiology) with data of other hospitals.Material and Methods. We performed retrospective cohort study in 727 patients (451 enrolled in primary center and 276 enrolled in other hospitals) admitted between June 24, 2014 and June 24, 2019. Refralon was administered for conversion of AFib and AFl in intense care units in escalating doses (10-30 micrograms/kg) intravenously.Results. Conversion of AFib and AFl into sinus rhythm was achieved in 53,6% after administration of 10 mcg/kg dose, in 73% after administration of 20 mcg/kg dose and in 91,6% after administration of Refralon in dose up to 30 mcg/kg. No mortality and no major adverse cardiac events registered in our study. Asystole >3.0 sec observed in 5% (35 of 727) of patients): in 5% (24 of 451) of patients enrolled in primary center and in 4% (11 of 276) of patients enrolled in other hospitals; 95% confidence interval (CI) [-0.09; 0.113]. Asystole> 5.0 s observed in 1.7% of patients who further required non-urgent implantation of a permanent pacemaker due to manifestations of sinus node dysfunction. Cardiac conduction disturbances (exclusively sinus bradycardia) were registered in 7% (53 of 727) patients: in 8% (37 of 451) of patients enrolled in primary center and in 6% (17 of 276) of patients enrolled in other hospitals; 95% CI: [-0.1; 0.15]. Only 0.14% of patients had symptomatic sinus bradycardia that resolved after atropine injection. Ventricular arrhythmias (exclusively Torsade de pointes tachycardia in excessive QT interval prolongation) were registered in 1.7% (12 of 727) patients: in 2% (9 of 451) of patients in primary center and in 1% (3 of 276) of patients of other hospitals; 95% CI: [-0.06; 0.08]. QTc interval prolongation to values >500 ms documented in 19% (138 of 727) of patients: in 21% (95 of 451) of patients in primary center and in 16% (43 of 276) of patients in other hospitals; 95% CI: [-0.13; 0.24].Conclusion: In post-registration multicenter trial Refralon demonstrated good safety profile in conversion of AFib and AFl. Potential risk of TdP tachycardia mandates precautions with the use of the drug. In other hospitals Refralon did not demonstrate lower safety than in primary medical center